cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A374881 Obverse convolution (n)**(n^2); see Comments.

Original entry on oeis.org

0, 1, 16, 405, 15360, 818125, 58226688, 5332085577, 610140160000, 85235284359225, 14264819712000000, 2815701027697558429, 646960843646287478784, 171112492588968115453125, 51595090958399913852928000, 17587698619968027952119140625
Offset: 0

Views

Author

Clark Kimberling, Jul 31 2024

Keywords

Comments

See A374848 for the definition of obverse convolution and a guide to related sequences.

Crossrefs

Programs

  • Mathematica
    s[n_] := n; t[n_] := n^2;
    u[n_] := Product[s[k] + t[n - k], {k, 0, n}]
    Table[u[n], {n, 0, 18}]

Formula

a(n) ~ n^(2*n + 1) / exp(2*n + 1 - Pi*sqrt(n)). - Vaclav Kotesovec, Jul 31 2024

A374886 Obverse convolution (n^2)**(n^3); see Comments.

Original entry on oeis.org

0, 1, 64, 10935, 3440640, 1819796875, 1496658788352, 1803211314966369, 3041248222904320000, 6927551870579340989625, 20704007211909120000000000, 79269804046766547371821983319, 381109146011936063547707158953984, 2261992022793941981178428306342521875
Offset: 0

Views

Author

Clark Kimberling, Sep 13 2024

Keywords

Comments

See A374848 for the definition of obverse convolution and a guide to related sequences.

Crossrefs

Programs

  • Mathematica
    s[n_] := n^2; t[n_] := n^3;
    u[n_] := Product[s[k] + t[n - k], {k, 0, n}]
    Table[u[n], {n, 0, 20}]

Formula

a(n) ~ exp(5/6 - 3*n - 4*Pi*n^(1/3)/3^(3/2) + 2*Pi*n^(2/3)/sqrt(3)) * n^(3*n + 17/6). - Vaclav Kotesovec, Sep 13 2024

A376524 a(n) = Product_{k=0..n} (k^4 + n - k).

Original entry on oeis.org

0, 1, 64, 12393, 6045696, 6332640625, 12659332976640, 44231711221193265, 252488580811970314240, 2232657903505428925782561, 29296905512056326144000000000, 550664857114160034501954633273625, 14393639721143326652705447551696896000
Offset: 0

Views

Author

Vaclav Kotesovec, Sep 26 2024

Keywords

Crossrefs

Programs

  • Mathematica
    Table[Product[k^4+n-k, {k, 0, n}], {n, 0, 16}]

Formula

a(n) ~ exp(sqrt(2)*Pi*n^(1/4) - 4*n) * n^(4*n + 5/2).
Showing 1-3 of 3 results.